Invariants
Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
Genus: | $3 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot10^{2}\cdot20^{2}$ | Cusp orbits | $2^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 20H3 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}23&110\\19&99\end{bmatrix}$, $\begin{bmatrix}33&100\\86&89\end{bmatrix}$, $\begin{bmatrix}43&40\\15&59\end{bmatrix}$, $\begin{bmatrix}81&20\\28&117\end{bmatrix}$, $\begin{bmatrix}87&80\\8&19\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.72.3.cge.2 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $16$ |
Cyclic 120-torsion field degree: | $512$ |
Full 120-torsion field degree: | $245760$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
40.72.1-20.b.1.9 | $40$ | $2$ | $2$ | $1$ | $0$ |
120.72.1-20.b.1.14 | $120$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
120.288.5-120.dn.2.11 | $120$ | $2$ | $2$ | $5$ |
120.288.5-120.ft.1.7 | $120$ | $2$ | $2$ | $5$ |
120.288.5-120.nf.1.3 | $120$ | $2$ | $2$ | $5$ |
120.288.5-120.ni.1.6 | $120$ | $2$ | $2$ | $5$ |
120.288.5-120.bch.2.3 | $120$ | $2$ | $2$ | $5$ |
120.288.5-120.bci.1.3 | $120$ | $2$ | $2$ | $5$ |
120.288.5-120.bco.1.3 | $120$ | $2$ | $2$ | $5$ |
120.288.5-120.bcp.1.8 | $120$ | $2$ | $2$ | $5$ |
120.288.5-120.blx.2.3 | $120$ | $2$ | $2$ | $5$ |
120.288.5-120.blz.2.8 | $120$ | $2$ | $2$ | $5$ |
120.288.5-120.bmk.2.2 | $120$ | $2$ | $2$ | $5$ |
120.288.5-120.bml.2.6 | $120$ | $2$ | $2$ | $5$ |
120.288.5-120.boh.2.3 | $120$ | $2$ | $2$ | $5$ |
120.288.5-120.boi.2.4 | $120$ | $2$ | $2$ | $5$ |
120.288.5-120.boo.2.2 | $120$ | $2$ | $2$ | $5$ |
120.288.5-120.bop.2.8 | $120$ | $2$ | $2$ | $5$ |
120.432.15-120.lo.2.12 | $120$ | $3$ | $3$ | $15$ |